288 Active Suspensions
m x “Skyhook damper” Figure 16.1. (a) One-DOF vehicle model
U mm with active suspension; (b) correspond-
ing LQG-optimal structure; and (c) pas-
S k sive one-DOF model (Hrovat 1988).
w w w
(a) (b)
(c)
versions. Thus, commercial implementations are primarily for low-bandwidth active
suspensions to emphasize attitude-holding performance during maneuvers and for
semi-active suspensions. Active stabilizer bars for roll control also have been imple-
mented. In semi-active suspensions, the damping forces can be adjusted by control
of the damping coefficient, for example, by using electro-rheological fluids.
In the following sections, the design of optimal, fully active, high-bandwidth
suspensions is described first based on a single DOF model, then on a two-DOF
model, and finally the optimal active suspension for the two-DOF model with state
estimation.
16.1 Optimal Active Suspension for Single-DOF Model
Consider the design of an active suspension based on the single-DOF model, as in
Figures 16.1a–c. As shown in Figure 16.3, we can define the two states x1 = suspension
stroke (positive in extension) and x2 = sprung-mass velocity (positive downwards).
The sprung mass is denoted by ms, the suspension force by u(t), and the ground-
velocity input by w(t). It is assumed that the ground-velocity input can be well
modeled as a zero-mean white-noise input, w, with variance W.
Normalized r.m.s. acceleration 100 ζ 2 DOF Figure 16.2. Comparison between perfor-
−5.15 + ∫5.15 mance of conventional passive suspension
for two-DOF vehicle model and optimal
10 one-DOF active suspension (with repre-
−2.29 ± ∫2.29 sentative eigenvalues) (Hrovat 1988).
1
1 DOF
0.1
0.01 1
Normalized r.m.s. suspension stroke
16.1 Optimal Active Suspension for Single-DOF Model 289
Figure 16.3. Single-DOF quarter-car model for active-suspension design. x
2
ms
x u
1
w
The equations of motion then are written as:
x˙1 = w − x2
u
x˙2 = − ms
In standard state equation form, these can be written as:
d x1 = 0 −1 x1 ⎡ 0⎤ 1 w
dt x2 0 0 x2 + ⎣− 1 ⎦ u + 0
ms
or
x˙ = Ax + bu + gw
As discussed in Chapter 4, the control-design objective can be represented as a
quadratic form in the states and control input. For example, if we consider a weighted
sum with weight r of the suspension stroke and control effort, we can write:
J = E x21(t ) + ru2(t ) = E x(t )T Rxxx(t ) + ru2(t )
From the Certainty Equivalence Principle, the optimal control gains are known to
be the same as for the corresponding deterministic LQ problem:
∞
J = x(t )T Rxxx(t ) + ru2(t ) dt
0
The optimal control is given by:
u∗(t ) = −r−1bT Px(t ) = −kTr x(t )
where P is the symmetric, positive-definite solution of the following algebraic Ricatti
equation:
AT P + PA − r−1PbbT P + Rxx = 0
For our problem, we solve the previous equation with:
0 −1 ⎧ 0 ⎫ P1 P2
0 0 ⎪ ⎪ P2 P3
⎨⎬
A= ; b= 1 ; P=
−
⎪ ms ⎪
⎩ ⎭
290 Active Suspensions
c= 1 −1
m 2 r 4
2 s
ms Figure 16.4. Optimal “skyhook damper” active suspension.
k = −1
r2
which yields:
P1 = 1 r 1 ; 1 P3 = √3 4
4 2ms2
2ms2 P2 = −msr 2 ; r3
and we then can obtain the optimal control:
u∗(t ) = −r−1bT Px(t ) = −kTr x(t )
√1
⎡ 2ms2 1 1 ⎤
4 2 ⎦
= −r−1 0− 1 r −ms r
ms x(t )
⎣ √3
−ms r 1 2ms2 r 3
2 4
= −r− 1 √1 r− 1 x(t ) = [k1 k2] x(t )
2 2ms2 4
Thus, the optimal control is a state-feedback controller:
u∗(t ) = −r− 1 √1 r 1 · x1
2 2ms2 4 x2
which feeds back – with optimal gains that depend on r and ms – the suspension stroke
x1 and the sprung-mass velocity x2. The physical interpretation of this control, as
shown in Figure 16.1b, is that of a passive suspension with a skyhook damper, which
is illustrated in Figure 16.4.
Consequently, the optimal active suspension cannot be implemented through
strictly passive means. In other words, it is not only the gains of the optimal controller
but also its structure, which is different from the passive suspension. As shown in
Figure 16.1c, the passive-suspension structure feeds back not x1 and x2 as in the
active suspension but rather x1 and x˙1.
16.2 Optimal Active Suspension for Two-DOF Model
Active suspension systems for automobiles also can be designed based on the two-
DOF quarter-car model for vertical motion (see Chapter 4) by using optimal con-
trol methods to achieve the desired tradeoffs among passenger comfort, packaging
requirements, and vehicle-handling requirements. This typically is accomplished by
using a quadratic performance criterion (similar to the one discussed in Example 4.9)
and a linear model of the vertical vehicle dynamics. The linear model was derived
previously in Chapter 4 and is given in Eqs. (4.63) and (4.64).
16.2 Optimal Active Suspension for Two-DOF Model 291
The controller design is based on the minimization of a quadratic performance
index including weighted combinations of the squares of the rms values of sprung-
mass acceleration, wheel hop, rattle space, and applied-force terms:
J = E x˙24 + r1x12 + r2x23 + r3u2 (16.1)
= x˙24rms + r1x12rms + r2 x23rms + r3ur2ms
= xTrmsRxxxrms + 2uxrTmsRxu + Ruuur2ms
where Ruu = (1 + r3):
⎡ r1 0 0 0⎤ ⎡0⎤
(2ζ2ω2 )2 −2ζ2ω23
⎢0 r2 + ω24 −(2ζ2 ω2 )2 ⎥ ⎢ −2ζ2ω2 ⎥
⎢ −2ζ2ω23 ⎥ ⎢ ω22 ⎥
Rxx = ⎢ −(2ζ2 ω2 )2 2ζ2ω23 Rxu = ⎢ ⎥ (16.2)
⎢ 0 2ζ2ω23 ⎥ ⎢ ⎥
⎥ ⎣ ⎦
⎣ ⎦
0 (2ζ2ω2 )2 2ζ2ω2
and the expectation operator, E, in Eq. (16.1) is defined by:
E{x(t )} = lim 1T x(τ )dτ (16.3)
T →∞ T 0
Other formulations of the performance index have been used – for example, includ-
ing jerk (i.e., time rate of change of the acceleration) as part of the passenger-comfort
criterion (Hrovat and Hubbard 1987).
Consider the design of an LQ optimal active suspension based on the model
shown in Chapter 4 and minimization of the performance index defined by Eqs.
(16.1) and (16.2) with respect to the control variable u(t). Initially, it is assumed
that all of the states, x(t), are measurable and can be used directly in the controller
implementation. Later, the implementation of the controller with measurement of
only some state variables is discussed. The LQ optimal controller is given by the
state-feedback law:
u(t )= −Krx(t ) (16.4)
where the optimal controller gain Kr is given by: (16.5)
Kr = R−uu1[B′P + R′xu]
and P is obtained from the solution to the algebraic Ricatti equation:
P(A − BR−uu1Rx′ u ) + (A′ − RxuR−uu1B′ )P − PBRu−u1B′P + Rxx − RxuR−uu1R′xu = 0
(16.6)
Equation (16.6) can be solved numerically using computer-aided-design software,
as illustrated in Example 16.1.
EXAMPLE 16.1: LQ ACTIVE-SUSPENSION DESIGN. An LQ active-suspension design
is illustrated in this example. The LQ controller design consists of selecting
weights for use in the performance index, then determining the controller gain
Kr. The MATLAB program also generates Bode Plots showing the response of
the system to a white-noise ground-velocity input, w(t). The Bode Plot includes
292 Active Suspensions
10−1 Frequency Response Magnitude Frequency Response Magnitude
10−2 Passive 100 Passive
10−3 Active 10−1 Active
100Tire def 10−2
Suspension stroke
10−3
101 102 103 10−4100 101 102 103
Frequency (rad/s) Frequency (rad/s)
102 Frequency Response Magnitude
101 Passive
Active
Sprung mass accel. 100
10−1 101 102 103
100 Frequency (rad/s)
Figure 16.5. Bode Plots of passive and active suspension systems.
frequency responses for the tire displacement, x1(t); the suspension stroke, x3(t);
and the sprung-mass acceleration, x˙4(t ). These results are in Figure 16.5, where
it can be seen that the active-suspension system achieves lower tire deflection
and sprung-mass acceleration in the low-frequency region, and its suspension
deflection is somewhat worse. The active suspension was found to improve
overall performance by about 17 percent.
% Ex16_1.m
clear
% Normalized vehicle parameters
w1 = 20*pi; % w1 = sqrt(kus/mus)
w2 = 2.0*pi; % w2 = sqrt(ks/ms)
z1 = 0.0; % z1 = cus/(2*ms*w1)
z2 = 0.3; % z2 = cs/(2*ms*w2)
rho = 10.0; % rho = ms/mus
% Passive system equations:
A = [0 1 0 0
-w1ˆ2 -2*(z2*w2*rho+z1*w1) rho*w2ˆ2 2*z2*w2*rho
16.2 Optimal Active Suspension for Two-DOF Model 293
0 -1 0 1
0 2*z2*w2 -w2ˆ2 -2*z2*w2];
B = [0 rho 0 -1]’; G = [-1 2*z1*w1 0 0]’;
% Define outputs for plotting results:
C= [1 0 0 0; % tire displacement
0 0 1 0; % suspension stroke
A(4,:)]; % sprung mass acceleration
Du = [0.0; 0.0; B(4)]; Dw = [0.0; 0.0; 0.0];
% Select weights for use in performance index:
% r1=1.1E3; r2=100.; r3=0.0; % Soft (S) ride case
r1=5.0e4; r2=5.0E3; r3=0.0; % Typical (T) ride case
% r1=1.0E6; r2=1.0E5; r3=0.0; % Harsh (H) ride case
Rxx = [r1 0 0 0
0 (2*z2*w2)ˆ2 -2*z2*w2ˆ3 -(2*z2*w2)ˆ2
0 -2*z2*w2ˆ3 (r2+w2ˆ4) 2*z2*w2ˆ3
0 -(2*z2*w2)ˆ2 2*z2*w2ˆ3 (2*z2*w2)ˆ2];
Rxu = [0 -2*z2*w2 w2ˆ2 2*z2*w2]’; Ruu = (1+r3);
% Calculate the LQ optimal gain Kr:
[Kr,S] = lqr(A,B,Rxx,Ruu,Rxu);
Ac=(A-B*Kr); Cc=(C-Du*Kr);
% Frequency response curves for the closed-loop and
% open-loop (passive) systems:
w=logspace(0,2.4,100);
[mag_p_tire, phase_p_tire] = bode(A,G,C(1,:),Dw(1),1,w);
[mag_a_tire, phase_a_tire] = bode(Ac,G,Cc(1,:),Dw(1),1,w);
[mag_p_susp, phase_p_susp] = bode(A,G,C(2,:),Dw(2),1,w);
[mag_a_susp, phase_a_susp] = bode(Ac,G,Cc(2,:),Dw(2),1,w);
[mag_p_ride, phase_p_ride] = bode(A,G,C(3,:),Dw(3),1,w);
[mag_a_ride, phase_a_ride] = bode(Ac,G,Cc(3,:),Dw(3),1,w);
loglog(w,mag_p_tire,‘r’,w,mag_a_tire,‘b-.’);
title(‘Frequency Response Magnitude’);
xlabel(‘Frequency (rad/s)’);
ylabel(‘Tire def’);
legend(‘Passive’, ‘Active’); pause
loglog(w,mag_p_susp,‘r’,w,mag_a_susp,‘b-.’);
title(‘Frequency Response Magnitude’);
xlabel(‘Frequency (rad/s)’);
ylabel(‘Suspension stroke’);
legend(‘Passive’, ‘Active’); pause
loglog(w,mag_p_ride,‘r’,w,mag_a_ride,‘b-.’);
title(‘Frequency Response Magnitude’);
xlabel(‘Frequency (rad/s)’);
294 Active Suspensions
ylabel(‘Sprung mass accel.’);
legend(‘Passive’, ‘Active’)
% calculate the performance index
% of the system with and without control
Xss=lyap(A,G*G’);
x3barrms=sqrt(Xss(3,3));
x1barrms=sqrt(Xss(1,1));
x4dotbarrms=sqrt([A(4,:)]*Xss*[A(4,:)]’+ [G(4)]*[G(4)]’);
Pindex=x4dotbarrmsˆ2+r1*(x1barrmsˆ2)+ r2*(x3barrmsˆ2);
Xss_act=lyap(Ac,G*G’);
x3barrms=sqrt(Xss_act(3,3));
x1barrms=sqrt(Xss_act(1,1));
x4dotbarrms=sqrt([Ac(4,:)]*Xss_act*[Ac(4,:)]’+ [G(4)]*[G(4)]’);
ubarrms=sqrt(Kr*Xss_act*Kr’); % control signal
Pindex_act=x4dotbarrmsˆ2+r1*(x1barrmsˆ2)+
r2*(x3barrmsˆ2)+r3*(ubarrmsˆ2);
% Ratio of active performance/passive performance
Pindex_act/Pindex
16.3 Optimal Active Suspension with State Estimation
A challenge in implementing state-feedback control algorithms, including the LQ
optimal-control approach, is that all states of the system must be measurable. From
a cost perspective, it is desirable to minimize the measurements needed for active-
suspension implementation. In such cases, some of the states required for the
feedback-control strategy are estimated from available measurements. This leads
to a so-called Linear Quadratic Gaussian (LQG) optimal control problem. The
unmeasured states are estimated using an optimal filter, known as the Kalman fil-
ter. The LQG optimal active-suspension design also is based on the quarter-car
model (i.e., Eqs. (4.63) and (4.64)); the performance index given in Eqs. (16.1)
and (16.2); and an output equation, which defines the measurable outputs of the
system:
y(t) =C x(t ) + Du(t ) (16.7)
where the coefficients C and D must be selected to define the measurable signals
that can be used in the controller. For example, if the suspension stroke, x3(t), is the
only measurable variable, then C and D in Eq. (16.7) become C = [0 0 1 0], and
D = 0. Similarly, if the measured variables are the suspension stroke, x3(t), and the
sprung-mass acceleration, x˙4(t ), then C and D in Eq. (16.7) become:
C= 0 0 1 0 ; D= 0 (16.8)
0 2ζ2ω2 −ω22 −2ζ2ω2 0
16.3 Optimal Active Suspension with State Estimation 295
where the second entry of the D matrix is obtained from the last entry of the input
matrix corresponding to the G matrix, which is the matrix for the road-velocity input.
The optimal LQG controller has the form:
u(t ) = −Krx⌢(t ) (16.9)
and Kr is calculated exactly from the same procedure as in the LQ control case. The
state estimates, x⌢(t ), are calculated from the equations:
d x⌢(t ) = Ax⌢(t ) + Bu(t ) + Ke(y(t ) − y⌢(t )) (16.10)
dt
and
y⌢(t ) = Cx⌢(t ) + Du(t ) (16.11)
The optimal estimator gain, Ke, is calculated from:
Ke = −PeCV−1
and Pe is computed from the solution of another algebraic Ricatti equation:
PeAT + APe − PeCV−1CTPe + W = 0 (16.12)
where V is the measurement-noise covariance matrix and W is the process-
disturbance covariance matrix. Like the weights Rxx, Ruu, and Rxu, these matrices
must be selected before the optimal estimator can be designed. The optimal esti-
mator relies more on the measurement by producing a large gain, Ke, when the
confidence in the measurement is high relative to the model (i.e., when V is small
compared to W). Similarly, when V is large compared to W, the estimator gain is
small and the estimates rely more on the model than the measurement.
For the closed-loop system, the state-space model has twice the number of state
variables as the open-loop system. When the plant model is completely known and
measurement noise is small, the state-space model of the augmented system is:
d x = A −BKr x + G w (16.13)
dt x⌢ KeC A − BKr − KeC x⌢ 0
When the “perceived” plant state and input matrices are different from those of the
true plant and measurement noise is included, the state-space model is:
x˙ = A −BKr x G0 w (16.14)
x⌢˙ x⌢ + 0 Ke v
⌢⌢ ⌢ ⌢
KeC A − BKr − KeC − Ke(D − D)Kr
⌢ ⌢⌢ ⌢
where A, B, C, and D are the perceived model matrices. Typically, the C and D
matrices are the same as the actual ones. In a case in which the feedback signal con-
tains acceleration terms, however, they might be different from the actual matrices.
It is important to note that because the augmented system has twice the number
of state variables as the original model, the output matrices all must be adjusted
accordingly. For example, when we want to obtain the actual tire-deflection signal,
the corresponding C matrix is C = [1 0 0 0; zeros(1,4)]. The estimated tire deflection,
conversely, is obtained from a C matrix that is C = [zeros(1,4); 1 0 0 0].
Yue, Butsuen, and Hedrick (1989) consider the LQG design of active suspen-
sions using only the suspension-stroke measurement. This LQG design approach
296 Active Suspensions
10−1 Frequency Response Magnitude 100 Frequency Response Magnitude
10−2 10−1
10−3 x3 only x3 only
x3 and x4 dot x3 and x4 dot
100
Tire def 10−2
Suspension stroke
10−3
101 102 10−4 101 102 103
Frequency (rad/s) 103 100 Frequency (rad/s)
Frequency Response Magnitude
x3 only
x3 and x4 dot
Sprung mass accel. 100
100 101 102 103
Frequency (rad/s)
Figure 16.6. Bode Plots of LQG active-suspension systems.
is illustrated in Example 16.2. Several possible measurement sets are considered in
Ulsoy et al. (1994. They also investigate the robustness of LQ and LQG controllers
with respect to unmodeled sensor and actuator dynamics and their sensitivity to
variations in the parameters of a parallel passive suspension.
EXAMPLE 16.2: LQG ACTIVE-SUSPENSION DESIGN. An LQG active-suspension
design, based only on suspension-stroke measurement, is illustrated in this exam-
ple. The LQG controller design consists of selecting the weights for use in the
performance index, selecting the covariance matrices for use in the Kalman fil-
ter, determining the controller gain Kr, and determining the estimator gain Ke.
The program also generates the Bode Plots showing the response of the closed-
loop system to a white-noise ground-velocity input, w(t). The results shown in
Figure 16.6 can be compared to those in Figure 16.5.
% Ex16_2.m
clear
% Specify model parameter values:
w1 = 20*pi; % w1 = sqrt(kus/mus); w2 = 2.0*pi;
% w2 = sqrt(ks/ms)
z1 = 0.0; % z1 = cus/(2*ms*w1); z2 = 0.3; % z2 = cs/(2*ms*w2)
rho = 10.; % rho = ms/mus
16.3 Optimal Active Suspension with State Estimation 297
% Open loop system equations:
A = [0 1 0 0
-w1ˆ2 -2*(z2*w2*rho+z1*w1) rho*w2ˆ2 2*z2*w2*rho
0 -1 0 1
0 2*z2*w2 -w2ˆ2 -2*z2*w2];
B = [0 rho 0 -1]’; G = [-1 2*z1*w1 0 0]’;
% Select weights for use in performance index:
% r1=1.1E3; r2=100.; r3=0.0; % Soft (S) ride case
r1=5.0e4; r2=5.0E3; r3=0.0; % Typical (T) ride case
% r1=1.0E6; r2=1.0E5; r3=0.0; % Harsh (H) ride case
Rxx = [r1 0 0 0
0 (2*z2*w2)ˆ2 -2*z2*w2ˆ3 -(2*z2*w2)ˆ2
0 -2*z2*w2ˆ3 (r2+w2ˆ4) 2*z2*w2ˆ3
0 -(2*z2*w2)ˆ2 2*z2*w2ˆ3 (2*z2*w2)ˆ2];
Rxu = [0 -2*z2*w2 w2ˆ2 2*z2*w2]’; Ruu = (1+r3);
% Calculate the LQ optimal gain Kr:
[Kr,S] = lqr(A,B,Rxx,Ruu,Rxu);
% Define C1 and D1 for suspension stroke
% Define C2 and D2 for sprung mass acceleration
C1=[0 0 1 0]; D1=0;
C2=[0 0 1 0;A(4,:)]; D2=[0;G(4)];
% parameters of the noise model:
Amp=1.65E-5; Vel=80; p=0.01;
% calculation of the covariances used in the KF design
Xss=lyap(A,G*G’);
x3barrms=sqrt(Xss(3,3));
x1barrms=sqrt(Xss(1,1));
x4dotbarrms=sqrt([A(4,:)]*Xss*[A(4,:)]’+ [G(4)]*[G(4)]’);
Pindex=x4dotbarrmsˆ2+r1*(x1barrmsˆ2)+ r2*(x3barrmsˆ2);
W=(2.0*pi*Amp*Vel);
V1=(pˆ2)*(2.0*pi*Amp*Vel)*(x3barrmsˆ2);
V2=(pˆ2)*(2.0*pi*Amp*Vel)*[(x3barrmsˆ2) 0; 0 (x4dotbarrmsˆ2)];
% calculation of the steady state KF gains
Ke1=lqe(A,G,C1,W,V1);
Ke2=lqe(A,G,C2,W,V2);
% Compute the state matrices for LQG systems
Ac1 = [A, -B*Kr; Ke1*C1, A-B*Kr-Ke1*C1];
Ac2 = [A, -B*Kr; Ke2*C2, A-B*Kr-Ke2*C2];
% Define various outputs for plotting results:
Cc_lqg = [1 0 0 0 0 0 0 0; % tire displacement
0 0 1 0 0 0 0 0; % suspension stroke
A(4,:) 0 0 0 0]; % sprung mass acceleration
Dw = [0.0; 0.0; G(4)]; Du = [0.0;0.0;B(4)]; Gc = [G;0;0;0;0];
% Frequency response
w=logspace(0,2.4,100);
[mag_p_tire, phase_p_tire] = bode(A,G,[1 0 0 0],0.0,1,w);
[mag_a1_tire, phase_a1_tire] = bode(Ac1,Gc,Cc_lqg(1,:),
Dw(1),1,w);
298 Active Suspensions
[mag_a2_tire, phase_a2_tire] = bode(Ac2,Gc,Cc_lqg(1,:),
Dw(1),1,w);
[mag_p_susp, phase_p_susp] = bode(A,G,[0 0 1 0],0,1,w);
[mag_a1_susp, phase_a1_susp] = bode(Ac1,Gc,Cc_lqg(2,:),
Dw(2),1,w);
[mag_a2_susp, phase_a2_susp] = bode(Ac2,Gc,Cc_lqg(2,:),
Dw(2),1,w);
[mag_p_ride, phase_p_ride] = bode(A,G, A(4,:), G(4),1,w);
[mag_a1_ride, phase_a1_ride] = bode(Ac1,Gc,Cc_lqg(3,:),
Dw(3),1,w);
[mag_a2_ride, phase_a2_ride] = bode(Ac2,Gc,Cc_lqg(3,:),
Dw(3),1,w);
loglog(w,mag_a1_tire,‘r’,w,mag_a2_tire,‘b-.’);
title(‘Frequency Response Magnitude’);
xlabel(‘Frequency (rad/s)’);
ylabel(‘Tire def’);
legend(‘x3 only’, ‘x3 and x4 dot’); pause
loglog(w,mag_a1_susp,‘r’,w,mag_a2_susp,‘b-.’);
title(‘Frequency Response Magnitude’);
xlabel(‘Frequency (rad/s)’);
ylabel(‘Suspension stroke’);
legend(‘x3 only’, ‘x3 and x4 dot’); pause
loglog(w,mag_a1_ride,‘r’,w,mag_a2_ride,‘b-.’);
title(‘Frequency Response Magnitude’);
xlabel(‘Frequency (rad/s)’);
ylabel(‘Sprung mass accel.’);
legend(‘x3 only’, ‘x3 and x4 dot’);
% calculate the rms response to a unit variance white
% noise input of the system with LQG control
Xss_a1=lyap(Ac1,[G;0;0;0;0]*[G;0;0;0;0]’);
x3barrms1=sqrt([0 0 1 0 0 0 0 0]*Xss_a1*[0 0 1 0 0 0 0 0]’);
x4dotbarrms1=sqrt([A(4,:) -B(4)*Kr]*Xss_a1*[A(4,:) -
B(4)*Kr]‘+[G(4)]*[G(4)]’);
x1barrms1=sqrt([1 0 0 0 0 0 0 0]*Xss_a1*[1 0 0 0 0 0 0 0]’);
ubarrms1=sqrt([0 0 0 0 Kr]*Xss_a1*[0 0 0 0 Kr]’);
Pindex_a1=x4dotbarrms1ˆ2+r1*(x1barrms1ˆ2)+r2*(x3barrms1ˆ2)
+r3*(ubarrms1ˆ2);
Xss_a2=lyap(Ac2,[G;0;0;0;0]*[G;0;0;0;0]’);
x3barrms2=sqrt([C1 0 0 0 0]*Xss_a2*[C1 0 0 0 0]’);
x4dotbarrms2=sqrt([A(4,:) -B(4)*Kr]*Xss_a2*[A(4,:) -
B(4)*Kr]‘+[G(4)]*[G(4)]’);
x1barrms2=sqrt([1 0 0 0 0 0 0 0]*Xss_a2*[1 0 0 0 0 0 0 0]’);
ubarrms2=sqrt([0 0 0 0 Kr]*Xss_a2*[0 0 0 0 Kr]’);
Pindex_a2=x4dotbarrms2ˆ2+r1*(x1barrms2ˆ2)+r2*(x3barrms2ˆ2)
+r3*(ubarrms2ˆ2);
Pindex_a1/Pindex
Pindex_a2/Pindex
16.3 Optimal Active Suspension with State Estimation 299
EXAMPLE 16.3: COMPARE PASSIVE, ACTIVE LQ, AND ACTIVE LQG SUSPENSIONS. The
responses of three suspension systems under the excitation of the same ground-
velocity input are compared in this example. The three suspensions compared
are the passive suspension, the active LQ suspension designed in Example 16.1,
and the active LQG suspension designed in Example 16.2. The responses for tire
deflection are compared in Figure 16.7a, for suspension stroke in Figure 16.7b,
and for sprung-mass acceleration in Figure 16.7c. The LQ and LQG results
are virtually indistinguishable. The active suspensions show some improvement
over the passive suspensions. These results also show the importance of working
with the rms values in the performance index because the time responses are
difficult to interpret in terms of performance.
% Ex16_3.m
clear; % Specify model parameter values:
w1 = 20*pi; % w1 = sqrt(kus/mus); w2 = 2.0*pi;
% w2 = sqrt(ks/ms)
z1 = 0.0; % z1 = cus/(2*ms*w1); z2 = 0.3; % z2 = cs/(2*ms*w2)
rho = 10.; % rho = ms/mus
% Open loop system equations:
A = [0 1 0 0
-w1ˆ2 -2*(z2*w2*rho+z1*w1) rho*w2ˆ2 2*z2*w2*rho
0 -1 0 1
0 2*z2*w2 -w2ˆ2 -2*z2*w2];
B = [0 rho 0 -1]’; G = [-1 2*z1*w1 0 0]’;
C= [1 0 0 0; % tire displacement
0 0 1 0; % suspension stroke
A(4,:)]; % sprung mass acceleration
Dw = [0.0; 0.0; G(4)]; Du = [0.0;0.0;B(4)];
% Select weights for use in performance index:
% r1=1.1E3; r2=100.; r3=0.0; % Soft (S) ride case
r1=5.0e4; r2=5.0E3; r3=0.0; % Typical (T) ride case
% r1=1.0E6; r2=1.0E5; r3=0.0; % Harsh (H) ride case
Rxx = [r1 0 0 0
0 (2*z2*w2)ˆ2 -2*z2*w2ˆ3 -(2*z2*w2)ˆ2
0 -2*z2*w2ˆ3 (r2+w2ˆ4) 2*z2*w2ˆ3
0 -(2*z2*w2)ˆ2 2*z2*w2ˆ3 (2*z2*w2)ˆ2];
Rxu = [0 -2*z2*w2 w2ˆ2 2*z2*w2]’; Ruu = (1+r3);
% Calculate the LQ optimal gain Kr:
[Kr,S] = lqr(A,B,Rxx,Ruu,Rxu);
% LQ results
Ac=(A-B*Kr); Cc=(C-Du*Kr);
% Define C1 and D1 for suspension stroke
% Define C2 and D2 for sprung mass acceleration
C1=[0 0 1 0]; D1=0;
C2=[0 0 1 0;A(4,:)]; D2=[0;G(4)];
% parameters of the noise model:
300 Active Suspensions
x 10−3 Tire Deflection
5
0 x1 (m)
−5x3 (m)
0 1 2 3 4 5 6 7 8 9 10
Time (sec)x4 dot x2 (m/sec)
Susp Stroke
0.04
0.03
0.02
0.01
0
−0.01
−0.02
−0.03
0 1 2 3 4 5 6 7 8 9 10
Time (sec)
Acceleration
1.5
1
0.5
0
−0.5
−1
−1.5
−2
0 1 2 3 4 5 6 7 8 9 10
Time (sec)
Figure 16.7. Simulation results of three suspension systems.
Problem 1 301
Amp=1.65E-5; Vel=80; p=0.01;
% calculation of the covariances used in the KF design
Xss=lyap(A,G*G’);
x3barrms=sqrt(Xss(3,3));
x1barrms=sqrt(Xss(1,1));
x4dotbarrms=sqrt([A(4,:)]*Xss*[A(4,:)]’+ [G(4)]*[G(4)]’);
Pindex=x4dotbarrmsˆ2+r1*(x1barrmsˆ2)+ r2*(x3barrmsˆ2);
W=(2.0*pi*Amp*Vel);
V1=(pˆ2)*(2.0*pi*Amp*Vel)*(x3barrmsˆ2);
V2=(pˆ2)*(2.0*pi*Amp*Vel)*[(x3barrmsˆ2) 0; 0 (x4dotbarrmsˆ2)];
% calculation of the steady state KF gains
Ke1=lqe(A,G,C1,W,V1);
Ke2=lqe(A,G,C2,W,V2);
% Compute the state matrices for LQG systems
Ac1 = [A, -B*Kr; Ke1*C1, A-B*Kr-Ke1*C1];
Ac2 = [A, -B*Kr; Ke2*C2, A-B*Kr-Ke2*C2];
% Define various outputs for plotting results:
Cc_lqg = [1 0 0 0 0 0 0 0; % tire displacement
0 0 1 0 0 0 0 0; % suspension stroke
A(4,:) 0 0 0 0]; % sprung mass acceleration
Gc = [G;0;0;0;0];
t=[0:0.1:10];
w=sqrt(2*pi*Amp*Vel)*randn(size(t));
yp=lsim(A,G,C,Dw,w,t);
ylq=lsim(Ac,G,Cc,Dw,w,t);
ylqg=lsim(Ac1,Gc,Cc_lqg-Du*[0 0 0 0 Kr],Dw,w,t);
clf; plot(t,[yp(:,1) ylq(:,1) ylqg(:,1)]);
title(‘Tire Deflection’);
xlabel(‘Time (sec)’); ylabel(’x1 (m)’); grid; pause;
plot(t,[yp(:,2) ylq(:,2) ylqg(:,2)]);
title(‘Susp Stroke’);
xlabel(‘Time (sec)’); ylabel(‘x3 (m)’); grid; pause;
plot(t,[yp(:,3) ylq(:,3) ylqg(:,3)]);
title(‘Acceleration’);
xlabel(‘Time (sec)’); ylabel(‘x4 dot (m/secˆ2)’); grid;
PROBLEMS
1. Rerun the MATLAB program in Example 16.1 to generate frequency-response
plots for the LQ active suspensions with soft, typical, and harsh ride characteristics.
Compare these plots and discuss why these particular combinations of the perfor-
mance index weights r1 and r2 are referred to as “soft,” “typical,” and “harsh.” For
these three LQ active suspensions and the passive-only suspension, create a table
that contains the following information: (a) the value of the performance index;
(b) the rms values of the individual terms in the performance index (e.g., suspension
302 Active Suspensions
stroke, tire deflection, and sprung-mass acceleration); and (c) the poles (or eigen-
values). Comment on how the various active designs change the values of these
quantities as compared to the passive case.
2. Use a MATLAB program similar to the one in Example 16.2 to design an LQG
active suspension that uses the “typical” ride weights, suspension-stroke measure-
ment, and both sprung-mass and unsprung-mass accelerations. Provide (a) frequency
response plots, (b) values of the performance index, and (c) closed-loop eigenvalues.
3. Your supervisor asks you to use a simple one-DOF quarter-car model to develop
an adaptive version of an active suspension based on RLS estimation. She wants
you to compare the performance of the adaptive active suspension to a nonadaptive
version in simulations in which the vehicle sprung mass can vary by ±50 percent
around its nominal value and to recommend whether adaptation is needed. The
model is given by:
∞
x J = x21 + ru2(t ) dt
2
ms 0
d x1 0 −1 x1 ⎡0⎤ 1
dt x2 0 0 x2 0
s = +⎣ 1 ⎦ u+ w
−
x u ms
1
w
where x1 is the suspension stroke, x2 is the sprung-mass velocity, and the output
y = the suspension stroke. Thus:
y = [1 0] x1 = x1
x2
The nonadaptive controller i√s an optimal c√ontrolle√r that minimizes J, given by u =
k1x1 + k2x2, where k1 = −(1/ r) and k2 = (2ms/ r). The model parameters have
nominal values of r = 0.0001 and ms = 1,500 kg. Thus, k1 = −100 and k2 = 547.723,
and the closed-loop eigenvalues are at s1,2 = −0.1826 ± 0.1826j for the nominal
conditions. However, because the sprung mass can vary, the actual closed-loop
performance also varies. Consequently, an adaptive, RLS-based, active suspension
based on this one-DOF quarter-car model also can be designed.
Note that for the plant-transfer function:
Y (s) 1
G(s) = U (s) = mss2
with a sampling period of h and a zero-order hold, the equivalent pulse-transfer
function is:
h2 z+1 z+1
H (z) = 2ms (z − 1)2 = α z2 − 2z + 1
References 303
Consequently, the discrete-time plant can be represented as:
⎧ y(k − 1) ⎫
⎪⎪
y(k) = [ 2 −1 α α ] ⎪ y(k − 2) ⎪
⎨ u(k − 1) ⎬
⎪ ⎪
⎪⎪
⎩ u(k − 2) ⎭
Formulate this as z(k) = θ Tf(k) in terms of unknown parameters θ . Then, the
RLS algorithm can be used to estimate the unknown parameters θ online from
measurements of y and u. The control gains can be updated accordingly. Assume a
sampling period of h = 1 second.
(a) Simulate the nonadaptive version of the active suspension for a unit-step
input w(t). Display the results for both suspension stroke and sprung-mass
acceleration for the nominal value of mass (i.e., typical vehicle load), the
maximum value of mass (i.e., fully loaded vehicle), and the minimum value
of mass (i.e., empty vehicle).
(b) Repeat the simulations in (a) but with an adaptive version of the active-
suspension design; compare the results to the nonadaptive version in (a).
What will you recommend to your supervisor?
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PART IV
INTELLIGENT TRANSPORTATION
SYSTEMS
17 Overview of Intelligent
Transportation Systems
Mobility is essential to the economic growth of any modern country and the well-
being of its population. This is especially true for the United States because of its size
and diffuse population. Without the efficient transport of people and goods, U.S.
industries cannot compete effectively with overseas producers. However, the rapid
growth in demand and the slower growth in the capacity of highway systems have
led to congestion that is estimated to cost more than $40 billion annually. In 1970,
motorists in the United States drove approximately 1 trillion vehicle-miles; by 1985,
this had increased to 1.8 trillion vehicle-miles; and, by 2000, to 2.8 trillion vehicle-
miles. These increases have led to serious congestion problems. For example, peak-
hour traffic operating in congested conditions on urban Interstate highways increased
from 40 percent in 1970 to nearly 70 percent in 1990. From 1982 to 2002, the vehicle-
miles traveled increased by 79 percent, whereas highway-lane miles increased by
only 3 percent. The number of roadways considered congested grew from 34 to
58 percent. However, construction of the more than 40,000 miles of the multilane,
controlled-access Interstate Highway System essentially is completed. Major new
construction, especially in dense urban areas, generally is not feasible and definitely
cannot keep up with future traffic demand. Although some growth of the highway
system is inevitable, the more efficient use of the existing system is essential.
In recent decades, there also have been tremendous changes in the areas of infor-
mation technology, electronics, computers, and communications. The pace of these
developments is simply astounding, and electronic devices have infiltrated every
aspect of life, including vehicles (see Chapter 1). Intelligent Transportation Systems
(ITS) (formerly known as Intelligent Vehicle Highway Systems [IVHS]), however,
represent more than simply advances in automotive electronics. ITS incorporate a
wide variety of electronic-based technologies, both on the vehicle and as part of the
highway infrastructure, which collectively are moving the world into the next gen-
eration of highway operations. These technologies offer the promise of increased
throughput on existing highways at reduced congestion levels as well as improved
safety and convenience. The ITS vision encompasses smart (i.e., control, sensing,
and communications) automobiles and highways collaborating for improved safety,
mobility, trip quality, and productivity while also reducing congestion and environ-
mental impact.
309
310 Overview of Intelligent Transportation Systems
ITS represents a long-term vision and an evolving concept of how the personal
automobile can continue to be a primary means of transportation despite the near
saturation of current highway capacities. Some argue that this is a dangerous vision
to meet transportation needs into the 21st century and that other high-speed public-
transportation systems must become an increasingly important part of the mix.
Nevertheless, it is clear that ITS technologies will have an important – even if not an
exclusive or primary – role in meeting transportation needs in the next few decades.
In many respects, the traffic-congestion problems faced today in the United
States are more severe in other parts of the world (e.g., Europe and Japan). Perhaps
it is not surprising then that Europe and Japan have taken a leadership role in the
development of ITS. A survey of ITS being tested worldwide is in Jurgen (1991),
and the situation relative to ITS in Japan is summarized in Ervin (1991). At the
Mobility 2000 Workshop (1990), ITS activities were grouped in the following four
major areas:
r Advanced Traffic Management Systems (ATMS)
r Advanced Traveler Information Systems (ATIS)
r Commercial Vehicle Operation (CVO)
r Advanced Vehicle Control Systems (AVCS)
Each of these areas is discussed briefly in the sections that follow (Special Issue on
IVHS 1991).
17.1 Advanced Traffic Management Systems
ATMS permit the real-time adjustment of traffic-control systems and variable-
message signs for drivers. Their application in selected corridors has reduced delay,
travel time, and accidents. Traffic-control systems have used control and communi-
cations technology for more than a half-century but have been slow to incorporate
the latest developments (e.g., distributed-system architecture, fiber-optic communi-
cations, and microprocessor-based equipment). The first traffic-control system using
analog technology to optimize a flow of traffic through a series of intersections was
installed in Chicago in 1926. It provided a fixed signal-timing sequence and did not
allow for variations in traffic-flow characteristics. The first digital, computer-based
system was installed in 1963 in Toronto; this system provided for more flexible signal
control by monitoring detectors as well as operation of the traffic-signal controllers
and detectors. Stored signal-timing plans were selected based on detector data or a
time-of-day basis. With the availability of reliable and inexpensive microprocessor
equipment in the 1980s, a form of signal control known as a “closed-loop system”
became available (Figure 17.1). A closed-loop system uses a central personal com-
puter that communicates with an intermediate level of control known as “master con-
trollers” or “local area masters.” These, in turn, communicate with the intersection
controllers. The master controllers reduce the processing load on the central com-
puter as well as the need to communicate directly with local intersection controllers.
ATMS require sensors in traffic lanes to identify the presence of vehicles and to
communicate that information to distributed or central processors. They depend
on real-time analysis of traffic data and systems for the control of traffic- and
ramp-metering signals. ATMS inform drivers about the status of traffic through
17.1 Advanced Traffic Management Systems 311
Information
Service Provider
traffic
information
Emergency incident notification Traffic incident data Roadway
Management incident information Management signage data
Roadway
Emergency Response TMC Incident Dispatch signal control data Signal Controls
Management Coord/Communication signal control status
emergency vehicle TMC Basic Signal
driver status update Control
Traffic
Maintenance
Emergency TMC
Vehicle Coord
Other TM
Figure 17.1. Information flow in closed-loop traffic-management systems.
variable-message signs. Ultimately, they indicate alternative routes to be followed
in case of a traffic incident. ATMS incorporate incident-management procedures,
which may reap the largest benefits. For example, an accident blocking one of three
lanes reduces highway capacity by 50 percent and a 20-minute blockage wastes
2,100 vehicle-hours. This can lead to a queue that is almost 2 miles long and can
take 2.5 hours to clear. During peak-traffic periods, the time wasted and delays
associated with accidents are 50 times worse. To be effective, systems require coop-
eration among adjacent jurisdictions to permit switching traffic from throughways
to arterials as required by incidents. Competent staff and maintenance crews are
required to ensure high-reliability systems. ATMS are being introduced with current
technology and will benefit from advanced technology. Wherever they have been
installed, they are reducing congestion by improving traffic flow and reducing acci-
dents and emissions (Table 17.1). The following lists the benefits of ramp-metering
Table 17.1. Benefits realized from implementation of ATMS
Location Reduced Reduced Accident Secondary Reduced Cost Delay
incident- response reduction accident accident savings/yr savings
clearance time (%) (%) reduction rates ($M) (hrs/yr)
time (%) (%)
Brooklyn, NY 66.0
Philadelphia, PA
San Antonio, TX 40.0 30.0 41.0% 1.65 255,500
Japan 20.0 35.0 50.0
Houston, TX 8.40 572,095
Denver, CO 0.95 95,000
Atlanta, GA 2,000,000
Minnesota 1.40
312 Overview of Intelligent Transportation Systems
and incident-management systems (Proper 1999):
r Portland, Oregon: 58 ramp meters, 43 percent accident reduction, 39 percent
travel-time reduction, 25 percent demand increase, 60 percent increase in speed
r Minneapolis/St. Paul, MN: 6 ramp meters, 8 km of freeway, 24 percent accident
reduction, 38 percent accident-rate reduction, 16 percent increase in speed
r Minneapolis, MN: 39 ramp meters, 27 km of freeway, 27 percent accident reduc-
tion, 38 percent demand increase, 35 percent increase in speed
r Seattle, WA: 22 ramp meters, 52 percent travel-time reduction, 39 percent
accident-rate reduction, 86 percent demand increase
r Denver, CO: 5 ramp meters, 50 percent accident reduction, 18.5 percent demand
increase
r Detroit, MI: 28 ramp meters, 50 percent accident reduction, 8 percent increase
in speed, 12.5 percent demand increase
r Austin, TX: 3 ramp meters, 4.2 km of freeway, 60 percent increase in speed, 7.9
percent demand increase
r Long Island, NY: 70 ramp meters, 207 km of freeway, 15 percent accident
reduction, 9 percent increase in speed
Thus, ATMS represent the highway side of the cooperative ITS concept. They
are being implemented in many major urban areas using existing technology that
can evolve as advanced technologies mature. An important feature in the future
development of ATMS is the ability to communicate with individual vehicles. This
discussion continues in the next two sections.
17.2 Advanced Traveler Information Systems
ATIS allow drivers and passengers to know the current location of their and other
vehicles and to find desired services. ATIS permit communication between the driver
and ATMS for continuous advice regarding traffic conditions, alternate routes, and
safety issues.
ATIS equipment can show vehicle location and movement on an electronic map.
This enables route planning from origin to destination, identification of businesses
or services that a driver may need, and the route to those sites. When ATIS and
ATMS are in full communication, drivers are informed of incidents and alternate
routes to avoid congestion. ATIS includes the following features:
r vehicle location (via GPS) and map-matching navigation system
r traffic-information receiver
r route planning for minimum distance of travel
r color video displays for maps, traffic information, and route guidance
r onboard database with detailed maps, business directory, specific location of
services, hospitals, and tourist information
r information from traffic-management centers about congestion, incidents, and
other problems
r electronic vehicle identification for toll debiting
Thus, ATIS represents the vehicle side of the cooperative ITS concept. Figure 17.2
shows information that was collected and used in ATIS services in the United States
17.2 Advanced Traveler Information Systems 313
50%
45%
40%
35%
30% Freeways
25% Arterials
20%
15%
10%
5%
0% Incidents Current work Scheduled work Weather
Traffic speeds Road conditions zones zones conditions
Types of information
Figure 17.2. 1999 transfer of information in ATIS services in the United States (Radin et al.
2000).
in 1999. ATIS is envisioned in the following three general stages of development in
North America:
r Information Stage. The primary emphasis is providing drivers with information
to improve individual planning and decision making.
r Advisory Stage. The static onboard information available to drivers is supple-
mented with dynamic traffic information collected and transmitted by the infra-
structure.
r Coordination Stage. Vehicles and infrastructure automatically exchange infor-
mation to optimize the flow and safety of traffic throughout the entire network.
Vehicle-navigation systems use the following three main technologies to determine
the location of a vehicle:
r GPS
r inertial navigation system (i.e., dead reckoning)
r map databases
Each has advantages and disadvantages that often are used in conjunction with one
another for best results. These systems can be used for in-vehicle route guidance,
route optimization, fleet management, and emergencies.
Various technologies are used to collect the data in ATIS, including video cam-
eras, surveillance systems, loop detectors, cellular phones, police patrol, and GPS,
as well as communications from transit authorities (e.g., road repairs) and updates
from private-sector firms (e.g., hotels and restaurants). The information can be pre-
sented to a driver using various technologies such as a cellular phone, cable TV,
314 Overview of Intelligent Transportation Systems
the Internet, e-mail, and an in-vehicle personal digital assistant (PDA). Commer-
cially available systems such as the GPS navigation systems, OnStar and Sync, are
examples of various ATIS capabilities.
17.3 Commercial Vehicle Operations
CVO select from ATIS those features critical to commercial and emergency vehicles.
They expedite deliveries, improve operational efficiency, and increase safety. CVO
are designed to interact with ATMS as both become fully developed.
Global competition is changing the way that companies conduct business. Car-
riers are expected to provide faster, more reliable, and more cost-effective services.
ITS technologies are emerging as a key to reducing costs and improving productivity.
Commercial and emergency vehicles will adopt ATIS and link them to ATMS as soon
as it is feasible to do so. Additional ITS technologies (some already have been devel-
oped) including weigh-in-motion sensors, automated vehicle-identification transpon-
ders, and automated vehicle-classification devices will reduce time spent in weigh
stations, reduce labor costs to states, and minimize red tape for commercial operators.
Commercial vehicles are leading the way in the development and implementation
of ITS technologies. They already are using automatic vehicle location, tracking,
and two-way communications; routing algorithms for dispatch; and in-vehicle text
and map displays. ITS technologies being used in commercial vehicles include the
following:
r automatic vehicle identification
r weigh-in-motion
r automatic vehicle classification
r onboard computer
r two-way, real-time communication
r automatic clearance sensing
Thus, CVO represents the vehicle side of the cooperative ITS concept for the special
needs of commercial and emergency vehicles. Figure 17.3 is a list of current and near-
future CVO devices on a commercial truck (Capps et al. 2001).
17.4 Advanced Vehicle-Control Systems
AVCS apply additional technology to vehicles to identify obstacles and adjacent
vehicles, thereby assisting in the prevention of collisions and resulting in safer oper-
ation at higher speeds. AVCS also may interact with the fully developed ATMS to
provide automated vehicle operations. A vision of the future of the automobile, in
which they drive themselves while the drivers relax, was first introduced in the Gen-
eral Motors pavilion at the 1939 World’s Fair. Since then, there have been relatively
few efforts aimed at realizing this vision. In 1979–1981, General Motors conducted
a systems study of highway automation (Bender 1991). In 1964–1980, studies on
vehicle guidance and control were conducted at Ohio State University (Fenton and
Mayhan 1991). In the same year, the University of California’s PATH program con-
ducted extensive studies on vehicle longitudinal and lateral control (Shladover et al.
1991).
17.4 Advanced Vehicle-Control Systems 315
Mobile Communications (voice and/or data) Company information and examples of products
for the above devices can be seen in FHWA’s
Automatic Vehicle Location Technology Truck, on the World Wide Web at
Automatic Toll http://www.ornl.gov/dp111/index.htm
Collection &
Screening - and at the Trucking Technology Magazine at
Transponders
http://www.truckingtechnologymag.com
On Board
Computers
Electronic scales Automatic
Equipment
Identification
Tire Pressure Monitoring
Vehicle Systems Monitoring
Engine Control Module, Fuel, Brake, K Common technology
Transmission Monitors
E Recently deployed technology
Accident Avoidance Systems Y Emerging technology
Figure 17.3. CVO devices on a commercial truck.
This section, an overview of AVCS technologies, identifies important classes of
problems and studies the potential benefits and impacts. Chapters 18 through 20
provide more detail on the following AVCS technologies: collision detection and
avoidance, longitudinal motion control and platooning, and lateral motion control
and automated steering.
The goal of AVCS is to enhance vehicle control by facilitating and augmenting
driver performance. Ultimately, AVCS aim to relieve drivers of most driving tasks.
Three levels of development are foreseen for AVCS technologies, as follows:
r ACVS-I: Individual vehicle control includes only vehicle-based systems that
detect the presence of obstacles or other vehicles. Studies show that half of
all rear-end collisions and as many as a third of intersection accidents can be
prevented if drivers have an additional half-second of warning. AVCS-I can
provide the additional warning time by sensing the presence of vehicles and
obstacles in blind spots. They also can warn drivers when their alertness starts
to wane.
r AVCS-II: Cooperative driver/vehicle/highway systems implement lateral and
longitudinal vehicle control functions in specific applications, such as high-
occupancy vehicle lanes. Vehicles enter the lane voluntarily using manual control
but then are under full or partial automatic control while in the lane. The advan-
tages include increased speed and safety. “Platooning,” the linking of cadre vehi-
cles, also is possible. For private vehicles, AVCS-II provides vehicle-to-vehicle
communication about travel paths, which will reduce collisions.
r AVCS-III: Automated vehicle-highway systems include complete automation
of the driving function for vehicles operating on specially equipped freeway
facilities. It builds on AVCS-I and AVCS-II technologies to provide “automated
chauffeuring” of vehicles from on-ramp arrival to off-ramp departure.
316 Overview of Intelligent Transportation Systems
Considerable research and development are needed before many AVCS technolo-
gies can be deployed commercially. Important areas for further research include the
following:
r availability and reliability of devices (i.e., ultrasonic, infrared, radar, and vision)
to detect spatial relationships of a vehicle to obstacles and other vehicles, and
the use of this information in the automatic control of vehicles
r the change in speed of a vehicle under automatic control to be compatible with
the limitations of human occupants and available equipment, and a facility for
extensive full-scale testing, including human-factor considerations
r special traffic lanes for AVCS-equipped vehicles and automatic inspection pro-
cedures to ensure that the AVCS are functioning before equipped vehicles can
enter them
It is anticipated that AVCS will reduce accidents and increase traffic flow; they
are predicted to double traffic flow on current freeways. These goals may seem
ambitious; however, development of the Interstate Highway System in the 1950s
and 1960s doubled lane capacity and reduced accidents by 60 percent by grade-
separating intersections and controlling access. AVCS technologies are described in
further detail in subsequent chapters.
As discussed previously, several stages of the evolution of AVCS technologies
are envisioned: beginning with in-vehicle control systems, which can detect the
presence of obstacles or other vehicles and warn the driver (i.e., AVCS-I); evolving
to partially automated driving systems on special high-occupancy vehicle lanes (i.e.,
AVCS-II); to fully cooperative vehicle–highway automation on major highways (i.e.,
AVCS-III). The human-factors aspect of the research is important to the successful
development of these proposed AVCS systems. Each phase is discussed in more
detail in the following subsections.
ACVS-I: Individual Vehicle Control
The goal of ACVS-I is to develop vehicle-based systems that detect the presence of
obstacles or other vehicles and that provide a warning to drivers. AVCS-I includes
only those advanced systems that are vehicle-based and that do not require inter-
vehicle or vehicle–highway communications and coordination. The principal benefits
of this technology are expected in the area of safety – that is, reductions in the
annual toll of crashes, fatalities, and injuries as well as the resulting economic costs.
However, AVCS-I technologies comprise the basis for the evolution to the AVCS-II
and AVCS-III phases.
In recent years, considerable advances have been made in sensing-, warning-, and
control-systems technologies with potential application to AVCS-I. The potential
for improved safety will be realized as follows:
r reduction in driver exposure to high-risk environments
r reduction in the incidence of high-risk driver behavior
r facilitation of earlier driver response to an imminent crash by providing addi-
tional seconds of warning time
17.4 Advanced Vehicle-Control Systems 317
r improvement in the overall speed and quality of driver–vehicle response in a
likely crash scenario
AVCS-I systems can be classified by the manner in which they aid a driver. Systems
that provide an enhanced image of the driving scene are referred to as “perceptual
enhancement” systems (e.g., night-vision systems). A driver is expected to interpret
the enhanced images and to control the vehicle in a manner that improves mobility
and safety. “Warnings” go one step further by providing an interpretation of sensor
signals (e.g., lane-departure warning). AVCS-I systems that alter control actions to
supplement those provided by a driver are referred to as “control enhancement”
systems (e.g., headway control in ACC systems).
AVCS-II: Cooperative Driver/Vehicle/Highway Systems
The goal of AVCS-II is to implement lateral and longitudinal vehicle control func-
tions in specific applications, such as high-occupancy vehicle lanes. Vehicles enter
lanes voluntarily under manual control but then are under full or partial automatic
control. The advantages are increased speed and safety; platooning also is possi-
ble. For private vehicles, AVCS-II offers vehicle-to-vehicle communication of travel
paths, which will reduce collisions.
AVCS-II requires both vehicle- and highway-based equipment and utilizes
vehicle-to-vehicle and roadway-to-vehicle communications systems developed in
ATMS and/or ATIS. Vehicle lateral and longitudinal position is controlled when
suitably equipped vehicles operate in dedicated instrumented lanes. Vehicles vol-
untarily enter and exit these lanes and under manual control but are under full
or partial system control while in them. The benefits include enhanced safety and
increased travel speed through bottleneck locations at a modest cost compared to
achieving the same benefit by increasing the number of parallel lanes. The specific
technological elements of AVCS-II, which provides a bridge between AVCS-I and
AVCS-III, include the following:
r automatic lateral control
r automatic longitudinal control
r vehicle-to-vehicle communications (e.g., for merge or demerge)
r system integration of AVCS-II technologies (e.g., platooning)
r intersection-hazard warning
r electric propulsion
Platooning is a principal focus of AVCS-II system development. When the first three
component technologies are combined, true driver/vehicle/highway platoon systems
can be developed. In platooning, vehicles are linked electronically into “platoons”
on one lane of a freeway. The first platooning facility likely consists of 20 to 25
miles of a two-lane freeway separated from other lanes by a barrier; a realistic
operation involves 5,000 to 10,000 vehicles. Systems required include a vehicle-to-
vehicle headway-control system, accurate vehicle-speed control, platoon-to-platoon
spacing control, and automated entrance diagnostics. Intersection-hazard warning
systems entail vehicle-to-vehicle communication about intended travel paths and
extend beyond the capabilities of obstacle-detection systems developed in AVCS-I.
318 Overview of Intelligent Transportation Systems
To reduce pollution in congested urban areas, roadway electrification and the use of
roadway-powered electric vehicles also is envisioned as a part of AVCS-II systems.
A short demonstration facility for an electrified roadway already operates, with a
single bus being used to test the concept at low speeds. High-occupancy vehicle lanes
that combine the use of electric vehicles and platooning are anticipated in congested
urban areas.
AVCS-III: Automated Vehicle–Highway Systems
The goal of AVCS-III is to achieve complete automation of the driving task on
limited-access highways. A limited demonstration of the concept has been successful
in California. The benefits of this system are derived from the application of the
following technologies as a complete package:
r drive-by-wire
r steer-by-wire
r automatic onboard diagnostics (which must be interrogated and found accept-
able before entry to AVCS-II facilities is permitted)
r automatic lateral control
r automatic longitudinal control
r vehicle-to-vehicle and vehicle-wayside communication for control
r human interfaces for transitions to and from control
r integration of automated roadways with arterials and local streets
r automatic traffic-merging control
r automatic lane-changing control
r automatic trip routing and scheduling
r automatic obstacle detection and avoidance
r reliability and safety enhancement features for all functions (e.g., real-time
condition monitoring, fault detection, and separate degraded performance and
emergency operating modes)
For both technical and environmental reasons, it also would be beneficial for vehicles
to be equipped with electric powertrains. Only a few elements of AVCS-III technol-
ogy are commercially available today, such as drive-by-wire (which is available on
only a few luxury vehicles).
There are no major technological barriers to the development of AVCS systems;
however, public acceptance is a major concern. Who will benefit from the technol-
ogy? How will the costs be allocated? Will AVCS systems be perceived as a threat to
contemporary lifestyles, privacy, or individual autonomy? What are the education
and training requirements for AVCS drivers? Safety is a major potential benefit
of AVCS systems but also increases risk if the systems do not work as intended.
Substantial effort in system design must be directed to minimizing the probability of
failures, as well as the consequences when failures do occur. It is difficult to antic-
ipate how the public will respond to AVCS, in which vehicles may be operating
in closer proximity and higher speeds than today. Much attention must be given
to the public’s emotional responses to this form of travel and its perceptions of its
safety.
References 319
PROBLEMS
1. The field of ITS is developing rapidly in terms of new technologies. Find a recent
article about one of the new developments and summarize the main points.
2. Find a Web site (e.g., through the local or regional department of transportation)
that provides information about how ITS technologies are being used in your region
and summarize the main points.
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18 Preventing Collisions
18.1 Active Safety Technologies
An important motivation for AVCS technologies is safety, and a key safety technol-
ogy is collision detection and avoidance systems. This type of safety enhancement
is termed “active safety,” which is different from the traditional passive-safety con-
cept (i.e., crashworthiness) (Sun and Chen 2010). The goal is to prevent collisions,
not simply mitigate their effects. There are two major driving forces behind recent
progress in the active-safety area, as follows:
1. The continuous progress in passive-safety systems has pushed the technology
into a return/cost plateau. For example, a recent study shows that 42 percent of
fatal-crash occupants can be saved by safety belts, and 47 percent can be saved
with safety belts plus an air bag (Figure 18.1). For the remainder of accidents, the
impact energy level is simply too high to be managed by reasonable engineering
means using current technology. Most of these high-impact energy impacts,
however, can be avoided altogether by active safety technologies (ASTs).
2. Recent changes in the standards for Corporate Average Fuel Economy (CAFE)
continue to move toward reduced petroleum consumption in the United States.
An important engineering approach for higher fuel efficiency is to lower vehicle
weight; however, this solution is likely to raise safety concerns. It has been veri-
fied consistently that vehicle weight is the third-most important safety attribute
for automobiles (i.e., after safety belts and air bags). Again, a possible solution
to this safety concern is to apply ASTs.
Many enabling technologies and subsystems, which are useful for AST, have
been widely available on passenger vehicles since 2005 (Table 18.1). Therefore,
the add-on complexity and cost of introducing AST are greatly reduced. This fact,
together with the obvious diminishing returns from passive-safety devices, has made
active-safety systems increasingly attractive.
18.2 Collision Detection and Avoidance
Human drivers do not always pay close attention to traffic conditions because of dis-
tractions (e.g., looking at the mirror, adjusting the radio, or using a cellular phone) or
322
18.2 Collision Detection and Avoidance 323
Table 18.1. Vehicle control functions and active safety technology (AST) enablement
Control function Installation base AST function
Cruise control 90% Throttle actuator
ABS 85% Automatic braking and yaw
TCS 20% Small deceleration and yaw
Electronically controlled transmissions 85% Down-shifting
Multiplex 35% Information and control
ACC 10% Range sensor
cannot react in a timely manner because of weather, lighting, or physical disabilities.
The value of collision detection and warning systems is in detecting hazardous situ-
ations and providing warning or intervention actions to avoid a collision or mitigate
damage. These systems require the sensing of objects in a vehicle’s near field and the
appropriate interpretation of the sensor signals for purposes of warning or control.
Also, this function must be carried out while a vehicle is traveling at a high speed. To
date, this difficult and important area has not been researched sufficiently. However,
there is considerable related research in areas such as obstacle avoidance in robot
trajectory planning and mobile robots. The problems, although clearly related, are
not identical because robots may not operate at high speeds and are not likely to
encounter other obstacles that may be moving at high speeds. Therefore, the vehi-
cle dynamics is important, whereas the robotic problems usually can be treated as
kinematic or even static problems. Also, robots must act autonomously on the infor-
mation obtained about obstacles. AVCS systems – at least AVCS-I and AVCS-II
systems – are expected to provide information on obstacles to a driver, or perhaps
warnings, but not to take over control of the vehicle. Studies show that many acci-
dents can be avoided if a driver has an additional 0.5 to 1 second in which to take
evasive action. Thus, the solution to the obstacle-detection and warning problem is
important and is expected to provide significant safety benefits.
One of the key enabling technologies for a collision detection and avoidance
system is the development of sensors. Ultrasonic, infrared, laser, video imaging, and
Fatality Prevention Effectiveness
+1190 lbs. 46% 200
+1050 lbs.
42% 0
Equal to –200 –140 lbs.
Added 18%
Vehicle –400
Weight
–600
+380 lbs.
–800
Unbelted Weight
Effects
with
Belt and
Air Bag
Air Bag Only Lap/ Belted
Shoulder with
Belted
Air Bag
Figure 18.1. Diminishing returns for passive safety systems.
324 Preventing Collisions
radar have been suggested as the most plausible sensing devices, some of which have
been demonstrated in applications The collision-detection functions are divided into
the following two general groups:
1. Near-obstacle detection: The application scenarios are low speed and/or low
range (i.e., rear and blind-spot detection). The detecting signals are usually wide
beam.
2. Forward-looking sensors and detection: For high-speed applications, the range
needs to be much higher than those for near-obstacle (e.g., approximately 300
versus 30 feet). The beam width is usually much narrower so that vehicles in
neighboring lanes are not constantly detected. For control-design purposes, it
is desirable to have both range and range-rate information. The same sensing
requirement can be used for ACC, which is one reason that the development of
forward-looking sensors has received significant attention.
Figure 18.2 illustrates a typical scenario for obstacle detection of a vehicle in a
highway environment. A long-range forward-looking detection system (e.g., radar)
could be coupled with a shorter range forward- and rear-obstacle detection system
(e.g., ultrasonic) or even a short-range side-detection system. Some blind spots may
remain depending on sensor placement and range. The presence of many stationary
roadside objects (e.g., trees and shrubs, guardrails, and signposts) increases the com-
plexity of the problem of processing sensor information. The use of computer vision
also has been considered but can be limited by computation times necessary for
image processing. In an ITS setting, some of these sensors may be on the highway
infrastructure – for example, induction coils or other vehicle detectors (Michigan
Department of Transportation 1981) – as well as on vehicles. The information avail-
able on a vehicle may be from its own near-field sensors and/or transmitted to it
from other vehicles and the roadway. For example, for merging maneuvers onto a
freeway, installing overhead vision systems at the on-ramp site used to signal vehicles
when it is safe to merge has been proposed (Pilutti et al. 1990). Such an overhead
vision system is being used in a SMART CRUISE demonstration project in Tsukuba
City, Japan, to monitor traffic flows for use in vehicle-navigation systems.
Ultrasonic sensors, already used in many applications such as autofocus cameras
and mobile robots, typically are limited to an approximate 10-meter range and are
not suitable for many highway applications. However, they may be useful (and have
been used) in vehicles for near-field obstacle detection at low speeds – for example,
to detect the curb in parallel parking and obstacles in a driveway when a driver is
backing out. The sensors can operate in conditions such as fog, smoke, and darkness
when visibility is poor. They also can be used in nonhighway vehicles, such as the
autonomous guided vehicles (AGVs) used in manufacturing plants and warehouses.
Radar is considered a leading obstacle-sensing technology for possible use in
automotive applications but there are important issues, including the appropriate
frequency band to be used, possible interference between similarly equipped vehi-
cles, and reflected radiation from road surfaces. Infrared sensors can be used to
supply range information. Alternatively, radar can be used to enhance a driver’s
perception – allowing for better visibility and longer reaction times – in night driving
and other conditions when visibility is poor. Prototype systems have been developed
and demonstrated for use with vehicles.
Lane
width
3.75m
0 50 100 [m] 200
Distance
Figure 18.2. Representative forward-looking sensor azimuth coverage
325
Lane 50 100 [m] 200
width
3.75m
0
e.
326 Preventing Collisions
When the range and possibly the range-rate information are obtained, the
collision-warning algorithm typically is triggered based on the following two types
of indexes, both of which are popular and used widely:
Time to Collision (TTC): The simple use of range over range rate gives a rea-
sonable index for collision warning. Depending on engineering judgment, this
index usually is selected to be between 5 and 8 seconds.
Safe Distance: Based on physics, a “safe following distance” d can be constructed,
which has the form:
d = Vctd + Vc2 − Vl2
2ac 2al
where Vc is the controlled (i.e., host) vehicle speed and td is the delay time,
which consists of human neuromuscular delay plus judgment time. Vl is the
lead vehicle speed and ac and al are deceleration limits, which usually are
assumed to be the same but can change with the environment (e.g., 4.5 m/sec2
for a dry road and 3.3 m/sec2 for a wet road).
Most collision-warning systems have multiple warning levels: the first level usu-
ally leaves judgment time for a driver to take action; the second level is triggered if a
threat becomes imminent. The second level may involve intervention – for example,
automated braking or differential braking (Pilutti et al. 1998) – as well as warnings
to the driver. Nevertheless, it is important that the driver maintain ultimate control
and be able to override any automated intervention.
Collision-avoidance systems consider and are developed for various scenarios,
such as longitudinal collisions, road-departure accidents, vehicle rollover, and
jackknifing of articulated vehicles. The TTC and safe-distance metrics described
previously are suitable for longitudinal (i.e., accelerating or braking) collision
scenarios. For single-vehicle road-departure (SVRD) accidents, which account for
nearly a fourth of all highway accidents and a third of all fatalities, other metrics such
as the time to lane crossing (TLC) are described in LeBlanc et al. (1996) and Lin and
Ulsoy (1996). Such systems also may require additional sensors – for example, to
measure yaw rate (Sivashankar and Ulsoy 1998) – and may include systems to assess
the driver state (Pilutti and Ulsoy 1999). Other active-safety systems address serious
scenarios such as vehicle rollover and jackknifing of trucks (Chen et al. 2010; Chen
and Peng 1999; Ma and Peng 1999b). The next generation of active-safety systems
for vehicles also is expected to include inter-vehicle communications, allowing for
the sharing of information among vehicles to achieve cooperative active-safety
systems (Caveney 2010).
EXAMPLE 18.1: PREVENTING RUN-OFF-ROAD ACCIDENTS. In this example (revisited
in Chapter 20), we consider an active-safety system to prevent SVRD accidents
(LeBlanc et al. 1996). The system is based on the TLC metric, which is computed
from two key elements (Lin and Ulsoy 1996): (1) a projection of the vehicle path;
and (2) an estimate of the upcoming lane geometry (Lin et al. 1999). A vision sys-
tem is used to look head and provide information about the upcoming roadway
geometry. On-vehicle sensors also are used to provide information about vehi-
cle motion, which then is used with a vehicle model and disturbance estimation
(Lin et al. 2000), such as in Eq. (4.49), to determine the path projection. Both
18.2 Collision Detection and Avoidance 327
File Model Simulation Disturbances Roadway Controllers Scenarios Window
CAPC Animation Near-field Camera Far-field Camera
CAPC Animation
0 100
t = 18.20
TLC = 1.83
WARNING !!
Figure 18.3. Simulation environment for design and evaluation of the SVRD active safety
system.
the path projection and the roadway-geometry estimation use Kalman filters
to best combine the sensor information with model information and to reduce
uncertainty in the TLC calculations.
When the TLC is below a certain threshold value, the system issues a warning
to the driver. This can be thought of as an “electronic rumble strip,” similar to
a physical rumble strip located along the edge of a highway that generates a
sound audible to the driver when the wheels are outside the lane edge (Pilutti
and Ulsoy 2003. These electronic rumble-strip systems have been implemented
in some long-range trucking vehicles, in which SVRD due to driver drowsiness
is a serious concern.
The system has the capability to not only warn the driver but, in some
cases, also to intervene or even fully control the vehicle when the driver is not
responsive. Therefore, the system includes the capability to assess driver status
(i.e., alert, drowsy, or unresponsive), which is accomplished by utilizing a driver
model. Input to the driver is assumed to be the view captured by the onboard
vision system and the output of the driver is the measured steering-wheel angle
(Pilutti and Ulsoy 1999). For example, if the camera detects a steady right turn
ahead and the driver does not respond by steering to the right, this indicates
that the driver is inattentive and may be drowsy or even asleep. In this case,
the system uses differential braking to generate a yaw moment (i.e., to steer the
vehicle to the right) (Pilutti et al. 1998).
As shown in Figure 18.3, a detailed simulation environment was used to develop
and evaluate this active safety system for preventing SVRD accidents. In addition,
328 Preventing Collisions
driving simulators and road tests were used to evaluate and refine the proposed
system.
PROBLEMS
1. A dead-reckoning system for vehicle navigation relies on integration of a velocity
signal to determine vehicle position:
t
x(t ) = v(τ )dτ + x(0)
0
If discrete-time measurements are made at time intervals, T, this can be approxi-
mated by:
t=NT
x(t ) = v(i)T + x(0)
i=0
The dead-reckoning approach can lead to position errors when there are errors in
the measured velocity values. Assume that the vehicle-measured velocity signal is
v(t) = sin(2π t) + e(t) and that T = 0.02. Consider the following cases and, for each
one, determine x(t = 0.5) given x(0) = 0:
(a) e(t) = 0 (i.e., no measurement error)
(b) e(t) = normal random error with zero mean and a standard deviation
of 1
(c) e(t) = 1.0 is a constant
Use MATLAB to compare and discuss the differences in the value of x(0.5) in each
case.
2. Consider a vehicle with velocity vf = 31 m/s that follows a lead vehicle with
velocity vl = 30 m/s at a distance of 10 m. The total delay time, td = 1 sec, and
acceleration/deceleration limits for both vehicles are af = al = 3 m. What are the
TTC and the safe distance? How do you interpret these metrics in the context of this
scenario?
3. Consider a simple scenario in which a vehicle is driving at constant longitudinal
velocity, u, along the centerline of a lane in a straight section of roadway (i.e.,
no curvature) with a constant heading angle, ψ. Assuming that u and ψ are both
measured exactly, show that the TLC can be calculated as:
TLC = ( / sin ψ )/u
References 329
where x is the distance along the lane, as shown in the following figure:
∆x
ψ
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19 Longitudinal Motion Control and Platoons
This chapter discusses the longitudinal control of vehicle motion in the context of
AVCS for ITS. It begins with a slightly refined version of a cruise-control system
with preview, which uses site-specific information available through the highway
infrastructure. It then builds on the ACC topic of Chapter 12 as an intermediate step
to the control of vehicles operating in platoons.
19.1 Site-Specific Information
It is assumed that highway infrastructure can provide information to drivers and vehi-
cles, which can be useful in numerous ways; for example, drivers can be warned of
accidents, roadwork, inclement weather or road-surface conditions, congestion, and
roadway characteristics such as grade and curvature. This already is being imple-
mented in many areas using programmable road signs on busy urban Interstate
highways (see Chapter 17). Here, we consider specifically the use of site-specific
information to improve the performance of vehicle control systems discussed in pre-
vious chapters. The manner in which such site-specific information can be provided
to a vehicle is discussed first and then the use of such information by vehicle control
systems.
Site-specific information can be provided to drivers and vehicles in a variety of
ways. For example, the Prometheus project in Europe uses transmitters on signposts
located along certain roadways in the Autocruise project to provide references to the
cruise-control system. A driver can choose to set the cruise-control system to pick up
speed-limit information transmitted from roadside signposts and then use this infor-
mation as the reference speed for the cruise-control system. Another concept for
providing site-specific roadside information, illustrated in Figure 19.1, involves the
use of message chips embedded in pavement and placed along a roadside or on road-
way bridges, overpasses, and signposts. The chips are similar to those already in use in
manufacturing plants and warehouses for inventory control and parts identification:
erasable programmable read only memory (EPROM) devices with a transmitter,
which can be reprogrammed remotely by authorized vehicles to update the infor-
mation they contain and transmit. These systems have been tested in under-the-
pavement and roadside use and demonstrated to be feasible. In both systems, there
are issues such as placement, range, durability, tamper-resistance, and power sources.
332
19.1 Site-Specific Information 333
Figure 19.1. Use of message chips to provide site-specific information.
Other key issues include: What kind of information should they contain and trans-
mit? How frequently should they be spaced? How “accurate” does the information
they transmit need to be? How often does the information need to be updated?
These issues require an understanding of the way in which the information may be
used and the potential benefits to be derived from its use.
Here, we consider use of site-specific information by the vehicle control sys-
tems. If it is available, can this information be used to improve the capabilities and
performance of in-vehicle control systems? The Autocruise system mentioned pre-
viously indicates that the answer may be affirmative. In that system, speed-limit
information is provided to the vehicle as a reference for the cruise-control system
and potentially relieves drivers of the need to reset the desired speed with changing
road conditions. Similarly, if road-roughness information is available, it may be used
by an active-suspension system to change automatically ride characteristics (e.g.,
soft versus typical versus harsh) rather than requiring drivers to make the selection.
Additional possibilities are as follows:
r Lane and road-curvature information could be provided for automated vehicle
lateral control, supplementing or alleviating the need for lane marking with
magnets or an onboard lane-sensing capability.
r Information on road-surface conditions (e.g., an icy bridge) could be provided
for use by TCS for antilock braking and anti-spin acceleration.
r Road-roughness information could be provided for use by the active-suspension
system not only to select ride characteristics but also to improve the control
algorithm by providing an estimate of the previously unknown road input.
r Altitude information could be useful for engine-control functions such as the
air–fuel ratio control.
r In addition to speed-limit information, road-grade information could be
useful for improving cruise-control-system performance, which is discussed in
Example 19.1.
EXAMPLE 19.1: CRUISE CONTROL WITH PREVIEW BASED ON SITE-SPECIFIC INFOR-
MATION. We first consider the use of site-specific information to improve the
performance of a simple cruise-control system (see Chapter 12). This assumes
that the highway infrastructure provides information to vehicles, specifically
road-grade information. Thus, if a vehicle can be warned of an upcoming grade,
the cruise control should be able to take advantage of this information to improve
speed-regulation performance. Figure 19.2 illustrates the open-loop system and
the closed-loop system (with PI control) block diagrams for a cruise-control
334 Longitudinal Motion Control and Platoons
θ θ Feedback
Openloop − mgsin(.) (PI control)
− mgsin(.) d+
F
d+ 1/c v vr + Ki + 1/c v
F (m/c)s + 1 - Kp + s (m/c)s + 1
+
Figure 19.2. Open-loop and example closed-loop cruise-control systems.
system (see Chapter 12). As a basis for comparison, the response of each system
to an uphill grade of θ = 10◦ is shown in Figure 19.3.
% Ex19_1.m
m=1000; c=85; g=9.8;
theta=pi/18;
K=1/c; tau=m/c;
disturb=-m*g*sin(theta);
Vd=25.0; Fo=Vd/K;
Ki=100.0; Kp=500; Ti=Kp/Ki;
vo(1)=Vd; vc(1)=Vd;
t(1)=0.0;
integ=Vd/(K*Ki); d=0.0;
tstep=0.1;
for i=1:999,
t(i)=i*tstep;
if i>300, d=disturb; end
vdot_o=[K*(Fo+d)-vo(i)]/tau;
vo(i+1)=vo(i)+vdot_o*tstep;
integ = integ + (Vd-vc(i))*tstep;
Fc=Kp*(Vd-vc(i))+Ki*integ;
vdot_c=[K*(Fc+d)-vc(i)]/tau;
vc(i+1)=vc(i)+vdot_c*tstep;
end
t(1000)=100.0;
plot(t,vo,t,vc), xlabel(‘Time (sec)’)
gtext(‘Openloop’)
gtext(‘PI control’)
30
25
PI control
20
15 Figure 19.3. Vehicle speed under gradient
disturbance.
Openloop
10
5
0 20 40 60 80 100
Time (sec)
19.1 Site-Specific Information 335
θˆ θ Feedback +
−mˆgsin(.)e −sT −mgsin(.) Feedforward
Control
vr + Ki dˆ + F d + 1/ c v
(m / c) s + 1
- Kp + s + +
Figure 19.4. Feed-forward and preview θˆ θ
control systems. f(mˆ, θˆ, T, p) −mgsin(.)
Feedback +
Preview
Control
vr + Ki dˆ + F d + 1/c v
- (m / c)s +1
Kp + s + +
Figure 19.4 illustrates two distinct ways in which the site-specific grade infor-
mation can be used (1) the use of feed-forward control together with the previous
PI feedback controller; and (2) a similar approach that uses a feed-forward action
based on preview (p) (i.e., advance knowledge of an upcoming grade). If our knowl-
edge of the vehicle parameters (m and c), grade disturbance ( ), and timing of
the grade (T) was exact, then the effect of the grade could be canceled exactly by
the feed-forward action, as shown in Figure 19.5a. However, these variables usually
are not exactly known, and a more realistic performance is shown in Figure 19.5b
for the feed-forward control strategy. Here, it is assumed that d is underestimated
by 10 percent and that there is a 1-second delay (T = 1) in the application of the
feed-forward compensation.
26
25.5 (a)PI + exact FF control
25 20 40 60 80 100
(b) PI + inexact FF control
24.5
20 40 60 80 100
Figure 19.5. Simulation results of PI + FF 24
cruise-control systems. 0
25.5
25
24.5
24
23.5
0
336 Longitudinal Motion Control and Platoons
25.4 PI + inexact preview control
25.2
Figure 19.6. Simulation results of PI + inexact pre-
25 view cruise-control system.
24.8
24.60 20 40 60 80 100
Time (sec)
% Ex19_1a.m
m=1000.0; c=85.0; g=9.8;
theta=pi/18.0;
K=1/c; tau=m/c;
disturb=-m*g*sin(theta);
disturb_h=disturb*0.9;
Vd=25.0;
Ki=100.0; Kp=500.0; Ti=Kp/Ki;
vc(1)=Vd;
t(1)=0.0;
integ=Vd/(K*Ki); d=0.0; d_h=0.0;
tstep=0.1;
for i=1:499,
t(i)=i*tstep;
if i>200, d=disturb; end
if i>210, d_h=disturb_h; end
integ = integ + (Vd-vc(i))*tstep;
Fc=Kp*(Vd-vc(i))+Ki*integ-d_h;
vdot_c=[K*(Fc+d)-vc(i)]/tau;
vc(i+1)=vc(i)+vdot_c*tstep;
end
t(500)=100.0;
plot(t,vc), xlabel(‘Time (sec)’)
title(‘PI + inexact FF control’)
With preview control, the driver anticipates that a grade is coming and begins
to increase vehicle speed before the grade is encountered. The preview is especially
important when the control signal does not affect the dynamics of the vehicle at the
same point, which is true in most cases. Figure 19.6 illustrates this strategy in which a
ramp preview signal is applied, starting 0.5 second before and ending 0.5 second after
the disturbance occurs. Again, the same inaccuracies used previously (i.e., 10 percent
underestimation) are used to obtain the results shown in Figure 19.6. It is clear
from these results that the preview control provides better performance in the case
of inexact knowledge. However, the improvements obtained by using site-specific
information are minor in this application and probably would not justify its use.
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Automotive control systems by Ali G Ulsoy Huei Peng Melih Çakmakci (z-lib.org)
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